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- Ivan I. Shevchenko, Nikolay N. Vasiliev
- ACM SIGSAM Bulletin
- 1993

It is suggested to derive formulae (dependences on symbolic parameters) by means of restoration upon a set of fixed exact numeric values of the parameters. The main tool is Pade interpolation. The problem of distortion of structure of restored expressions and, to some extent, the problem of verification of results are considered. A statistical treatment of… (More)

- Ivan I. Shevchenko, Andrej G. Sokolsky
- ISSAC
- 1993

The perturbed motion in the neighborhood of regular precession of a dynamically symmetric satellite on a circular orbit is studied. The “Norma” specialized program package [1,2], intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian. A full catalogue of non-resonant and… (More)

- Ivan I. Shevchenko
- Computer Physics Communications
- 2008

- Ivan I. Shevchenko
- J. Symb. Comput.
- 1997

Algorithms of numeric (in exact arithmetic) deduction of analytical expressions, proposed and described by Shevchenko and Vasiliev (1993), are developed and implemented in a computer algebra code. This code is built as a superstructure for the computer algebra package by Shevchenko and Sokolsky (1993a) for normalization of Hamiltonian systems of ordinary… (More)

- Ivan I Shevchenko
- Physical review. E, Statistical, nonlinear, and…
- 2010

We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit Lévy flights. Due to them, the time decay of the survival probability is heavy-tailed with the power-law index equal to -2/3, while the… (More)

- E L Mordberg, I I Shevchenko, A F Arkhipov
- Gigiena i sanitariia
- 1981

- Ivan I Shevchenko
- Physical review. E, Statistical, nonlinear, and…
- 2012

Modern theoretical methods for estimating the width of the chaotic layer in the presence of prominent marginal resonances are considered in the perturbed pendulum model of nonlinear resonance. The fields of applicability of these methods are explicitly and precisely formulated. The comparative accuracy is investigated in massive and long-run numerical… (More)

- I Iu Shevchenko
- Gigiena i sanitariia
- 2008

The paper analyzes the time course of changes in the intake of staple foods in the Krasnoyarsk Territory in 1998-2005. It is shown that the ingestion of iodine-rich foods has not increased greatly and it is low and does not provide the population with this essential micronutrient. The actual content of iodine in the study samples of food and its raw… (More)

- I. I. Shevchenko
- 2008

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. An especially designed software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian in the given problem. The normalization is… (More)

- E L Mordberg, I I Shevchenko, N A Pokkova
- Gigiena i sanitariia
- 1984